本研究採用參數化之泛密度函數緊密捆綁(Density Functional Tight Binding, DFTB)理論，計算電中性金叢集之力場，并結合了布朗式(Brownian-type)分子動力學演算法[S. K. Lai, W. D. Lin, K. L. Wu, W. H. Li, and K. C. Lee, J. Chem. Phys. 121, 1487 (2004)]，針對該系統在Nosé-Hoover恆溫系統下之情況，進行模擬與研究。首先，我們在溫度於300K對所預備之四組金叢集進行模擬數據分析，從其熱力動力效應中推斷出它們的(a)結構流動性(b)鏡像對稱，與(c)二維到三維的變相現象。在所有分子動力學實驗模擬中，其所使用之叢集的離子各初始坐標位置是透過一套個別的優化演算法[T.W. Yen, T.L. Lim, T.L. Yoon and S.K. Lai, Comput. Phys. Commun. 220, 143 (2017)]取得。該優化演算法可在各別的叢集能量函數中使用DFTB理論獲取最低能量之結構。而應用同樣的初始結構模式，本文也在300K溫度中獨立地進行亞穩動力之分子動力學（MMD）模擬，與此同時在三組叢集裏使用集體變量（collective variable, CV） 空間，而不是以離子的位置坐標表示的傳統配置空間，來產生偏能軌跡。這MMD模擬旨在探索金叢集在CV 空間裏之時間性變化。
我們透過DFTB理論架構下所計算之能量函數的叢集分析結果，與應用一經驗勢(empirical potential)理論所得之MMD模擬結果作爲比較。這經驗勢是透過塊材固態數據來決定能勢參數。我們期待這樣的對照能揭示s-d 混成軌域在金叢集的電子與結構特徵所扮演的微妙和重要角色。
總結來説，本文深入探討所選之叢集的若共價行爲，同時也檢驗以上所描述在布朗式分子動力學與 MMD 模擬裏的(a)至(c)現象。

The parametrized density functional tight-binding (DFTB) theory is used to calculate the force field of a neutral gold cluster and it is then combined with the Brownian-type molecular dynamics (MD) algorithm [S. K. Lai, W. D. Lin, K. L. Wu, W. H. Li, and K. C. Lee, J. Chem. Phys. 121, 1487 (2004)] to perform simulation studies for this system within the Nosé-Hoover thermostat scheme. We analyze the simulation data for four selected Au clusters which were prepared at T=300 K, and deduce from their thermally evolved behaviors the (a) fluxional character, (b) chiral behavior, and (c) traits of the bi- to tridimensional transition. In all of these MD simulations studies, the initial input position coordinates of ions in these clusters were the lowest energy configurations which we obtained separately from an optimization algorithm [T.W. Yen, T.L. Lim, T.L. Yoon and S.K. Lai, Comput. Phys. Commun. 220, 143 (2017)] where the individual cluster’s energy function employed is within the same DFTB theory. Using these same initial structures, we carried out also independent metadynamics MD (MMD) simulations at 300 K and generated biased trajectories for two of these selected clusters in a collective-variable space instead of the conventional configurational space in terms of the position coordinates of ions. The MMD simulations serve to explore the temporal change of Au clusters in the collective-variable space. It is hoped that an analysis of clusters whose energy functions are calculated in the DFTB theory in the latter and the comparison of simulation results with similar MMD simulations conducted with an empirical potential whose potential parameters are determined from bulk solid-state data would shed light on the subtlety and importance of s-d hybridization which is known to play an important role in both the electronic and structural properties of Au clusters. In this work, we delve into the effects of this covalent-like behavior of these selected clusters, examining them in parallel the features (a)-(c) mentioned above in Brownian-type MD and MMD simulations.

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